Editing Key signature (section)

=== Double flats and sharps ===
[[Key signatures]] can extend into [[double flat]]s or [[double sharp]]s, but this is extremely rare. For example, the key of [[G sharp major|G{{music|#}} major]] would have eight sharps, requiring an F double-sharp (F{{music|x}}) and six single sharps. The key of [[A flat major|A{{music|b}} major]], with four flats, is [[Enharmonic equivalence|enharmonically equivalent]] and would generally be used instead. Although this system of notation could theoretically continue to be extended beyond single flats or sharps, a key signature with more than one or two double flats or sharps would be exceedingly hard to read and would be replaced by the enharmonically equivalent key signature.
{| class="wikitable"
![[Major key|Major]]
!Key signature
![[Minor key|Minor]]
|-
|[[F-flat major|F{{Music|flat}} major]] ([[E major]])
|8 flats (4 sharps)
|[[D-flat minor|D{{Music|flat}} minor]] ([[C-sharp minor|C{{Music|sharp}} minor]])
|-
|B{{Music|doubleflat}} major ([[A major]])
|9 flats (3 sharps)
|G{{Music|flat}} minor ([[F-sharp minor|F{{Music|sharp}} minor]])
|-
|E{{Music|doubleflat}} major ([[D major]])
|10 flats (2 sharps)
|C{{Music|flat}} minor ([[B minor]])
|-
|A{{Music|doubleflat}} major ([[G major]])
|11 flats (1 sharp)
|F{{Music|flat}} minor ([[E minor]])
|-
|D{{Music|doubleflat}} major ([[C major]])
|12 flats (no flats or sharps)
|B{{Music|doubleflat}} minor ([[A minor]])
|-
|G{{Music|doubleflat}} major ([[F major]])
|13 flats (1 flat)
|E{{Music|doubleflat}} minor ([[D minor]])
|-
|C{{Music|doubleflat}} major ([[B-flat major|B{{Music|flat}} major]])
|14 flats (2 flats)
|A{{Music|doubleflat}} minor ([[G minor]])
|-
|[[G-sharp major|G{{Music|sharp}} major]] ([[A-flat major|A{{Music|flat}} major]])
|8 sharps (4 flats)
|[[E-sharp minor|E{{Music|sharp}} minor]] ([[F minor]])
|-
|D{{Music|sharp}} major ([[E-flat major|E{{Music|flat}} major]])
|9 sharps (3 flats)
|B-sharp minor|B{{Music|sharp}} minor ([[C minor]])
|-
|A{{Music|sharp}} major ([[B-flat major|B{{Music|flat}} major]])
|10 sharps (2 flats)
|F{{Music|doublesharp}} minor ([[G minor]])
|-
|E{{Music|sharp}} major ([[F major]])
|11 sharps (1 flat)
|C{{Music|doublesharp}} minor ([[D minor]])
|-
|B{{Music|sharp}} major ([[C major]])
|12 sharps (no flats or sharps)
|G{{Music|doublesharp}} minor ([[A minor]])
|-
|F{{Music|doublesharp}} major ([[G major]])
|13 sharps (1 sharp)
|D{{Music|doublesharp}} minor ([[E minor]])
|-
|C{{Music|doublesharp}} major ([[D major]])
|14 sharps (2 sharps)
|A{{Music|doublesharp}} minor ([[B minor]])
|}
A piece in a major key might modulate up a [[Perfect fifth|fifth]] to the [[Dominant (music)|dominant]] (a common occurrence in Western music), resulting in a new key signature with an additional sharp. If the original key was C-sharp, such a [[Modulation (music)|modulation]] would lead to the key of G-sharp major (with eight sharps) requiring an F{{Music|x}} in place of the F{{Music|#}}. This section could be written using the enharmonically equivalent key signature of A-flat major instead. [[Claude Debussy]]'s ''[[Suite bergamasque]]'' does this: in the third movement "Clair de lune" the key shifts from D-flat major to D-flat minor (eight flats) for a few measures but the passage is notated in C-sharp minor (four sharps); the same happens in the final movement, "Passepied", in which a G-sharp major section is written as A-flat major.

Such passages may instead be notated with the use of double-sharp or double-flat accidentals, as in this example from [[Johann Sebastian Bach]]'s ''[[Well-Tempered Clavier]]'', which has this passage in G-sharp major in measures 10-12.

[[File:G-sharp major example 2.png]]

While these keys are sometimes notated with accidentals as in this example, the use of a key signature containing double flats or sharps is very rare. The final pages of [[John Foulds]]' ''[[A World Requiem]]'' are written in [[G-sharp major|G♯ major]] (with F{{music|x}} in the key signature), No. 18 of [[Anton Reicha]]'s ''Practische Beispiele'' is written in B{{music|#}} major, and the third movement of [[Victor Ewald]]'s [[Brass quintet|Brass Quintet]] Op. 8 is written in [[F♭ major]] (with B{{music|bb}} in the key signature).<ref name=":0">{{IMSLP|work=Practische Beispiele (Reicha, Anton)|cname=Anton Reicha: ''Practische Beispiele'', pp. 52-53.}}</ref><ref>{{cite web |author=<!--Staff writer(s); no by-line.--> |title=Ewald, Victor: Quintet No 4 in A{{music|b}}, op 8 |url=http://www.enspub.com/pages/93/93503.htm |access-date=14 February 2023 |publisher=imslp}}</ref>

Examples of such key signatures are pictured below:<score>
\relative c' { \omit Staff.TimeSignature \omit Staff.KeyCancellation
  \key gis \major <gis' bis dis><eis gis bis>_\markup \halign #0.2 \center-column { "G♯ maj" "E♯ min" } \bar "||"
  \key dis \major <dis fisis ais><bis dis fisis>_\markup \halign #0.2 \center-column { "D♯ maj" "B♯ min" } \bar "||"
  \key fes \major <fes' as ces><des fes as>_\markup \halign #0.2 \center-column { "F♭ maj" "D♭ min" } \bar "||"
  \key beses \major <beses' des fes><ges beses des>_\markup \halign #0.2 \center-column { "B♭♭ maj" "G♭ min" }
}
</score>There does not appear to be a standard on how to notate these key signatures:

* The default behaviour of [[LilyPond]] (pictured above) writes all single sharps or flats in the circle-of-fifths order before showing the double signs. This is the format used in [[John Foulds]]' ''[[A World Requiem]]'', Op. 60, which uses the key signature of G♯ major as displayed above.<ref>{{IMSLP|work=A World Requiem, Op.60 (Foulds, John)|cname=John Foulds: ''A World Requiem'', pp. 153ff.}}</ref> The sharps in the key signature of [[G-sharp major|G♯ major]] proceed C♯, G♯, D♯, A♯, E♯, B♯, F{{music|x}}.
* The single signs at the beginning are sometimes repeated as a courtesy, e.g. [[Max Reger]]'s ''Supplement to the Theory of Modulation'', which contains [[D♭ minor]] key signatures on pp.&nbsp;42–45.<ref>{{cite book |author=Max Reger |title=Supplement to the Theory of Modulation |publisher=C. F. Kahnt Nachfolger |year=1904 |location=Leipzig |pages=[https://archive.org/details/supplementtotheo00rege/page/42/mode/2up 42–45] |translator=John Bernhoff}}</ref> These have a B♭ at the start and also a B{{music|bb}} at the end (with a double-flat symbol), going B♭, E♭, A♭, D♭, G♭, C♭, F♭, B{{music|bb}}.
* Sometimes the double signs are written at the beginning of the key signature, followed by the single signs. For example, F♭ would be notated as B{{music|bb}}, E♭, A♭, D♭, G♭, C♭, F♭. This convention is used by Victor Ewald<ref>[https://www.hickeys.com/music/brass/brass_ensembles/brass_quintets/products/sku035994-ewald-victor-quintet-no-4-in-ab-op-8.php "Ewald, Victor: Quintet No 4 in A{{music|b}}, op 8"], Hickey's Music Center</ref> and by some theoretical works.
* No. 18 of Anton Reicha's ''Practische Beispiele'' in B♯ major<ref name=":0" /> shows B♯, E♯, A{{music|x}}, D{{music|x}}, G{{music|x}}, C{{music|x}}, F{{music|x}}.

In [[tuning system]]s where the number of notes per octave is not a multiple of 12, notes such as G{{music|#}} and A{{music|b}} are not enharmonically equivalent, nor are the corresponding key signatures. These tunings can produce keys with no analogue in 12-tone equal temperament, which can require double sharps, double flats, or [[microtonal music|microtonal alterations]] in key signatures. For example, the key of G♯ major, with eight sharps, is equivalent to A{{music|b}} major in 12-tone equal temperament, but in [[19 equal temperament|19-tone equal temperament]], it is equivalent to A{{Music|bb}} major instead, with 11 flats.